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A247636
Numbers k such that d(r,k) != d(s,k), where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.
2
1, 3, 4, 5, 6, 7, 12, 13, 15, 19, 21, 23, 25, 27, 29, 36, 38, 41, 42, 46, 48, 50, 52, 53, 55, 56, 60, 61, 64, 65, 66, 68, 70, 71, 72, 77, 78, 80, 83, 84, 86, 88, 89, 91, 93, 95, 96, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 112, 113, 118
OFFSET
1,2
COMMENTS
Every positive integer lies in exactly one of the sequences A247635 and A247636.
LINKS
EXAMPLE
r has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, ...
s has binary digits 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, ...
so that a(1) = 1 and a(2) = 3.
MATHEMATICA
z = 200; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[8]];
u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]];
v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]];
t = Table[If[u[[n]] == v[[n]], 1, 0], {n, 1, z}];
Flatten[Position[t, 1]] (* A247635 *)
Flatten[Position[t, 0]] (* A247636 *)
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Clark Kimberling, Sep 23 2014
STATUS
approved